Density Forecast Combinations: The Real-Time Dimension

Abstract

Density forecast combinations are examined in real-time using the log score to compare five methods: fixed weights, static and dynamic prediction pools, as well as Bayesian and dynamic model averaging. Since real-time data involves one vintage per time period and are subject to revisions, the chosen actuals for such comparisons typically differ from the information that can be used to compute model weights. The terms observation lag and information lag are introduced to clarify the different time shifts involved for these computations and we discuss how they influence the combination methods. We also introduce upper and lower bounds for the density forecasts, allowing us to benchmark the combination methods. The empirical study employs three DSGE models and two BVARs, where the former are variants of the Smets and Wouters model and the latter are benchmarks. The models are estimated on real-time euro area data and the forecasts cover 2001–2014, focusing on inflation and output growth. We find that some combinations are superior to the individual models for the joint and the output forecasts, mainly due to over-confident forecasts of the BVARs during the Great Recession. Combinations with limited weight variation over time and with positive weights on all models provide better forecasts than those with greater weight variation. For the inflation forecasts, the DSGE models are better overall than the BVARs and the combination methods.

Keywords: Bayesian inference, euro area, forecast comparisons, model averaging, prediction pools, predictive likelihood

JEL Classification: C11, C32, C52, C53, E37